write the equation of the following:

Question

Answer 1

The left portion of the graph looks like a parabola with a zero at -3 having multiplicity 2 which means it will result in a factor of (x + 3)².

The middle portion of the graph looks like x³.

The right side of the graph has a zero of 2 so a corresponding factor of (x - 2).

Putting these together we have (x + 3)²(x³)(x - 2)

There will be a negative stretch factor but we can let the algebra determine the value. Since the point (-2, -8) is on the graph, we can say:

-8 = a((-2) + 3)²((-2)³)((-2) - 2)

-8 = a(1)² (-8)(-4)

-8 = 32a

a = -8/32 = -1/4

So f(x) = -1/4(x + 3)²(x³)(x - 2)

Of course, if desired, this can be multiplied out to provide a polynomial in standard form.